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On Compactness of Commutators of Multiplications and Fourier Multipliers

  • Nenad AntonićEmail author
  • Marin Mišur
  • Darko Mitrović
Article
  • 56 Downloads

Abstract

We generalise results on compactness of commutators of multiplications and Fourier multiplier operators by Cordes (J Funct Anal 18:115–131, 1975) with respect to the smoothness of multiplication function. Our prime motivation has been a particular case known as the first commutation lemma—the basic tool for defining H-measures and H-distributions. We review and improve the known results in the \(\mathrm{L}^p\) setting, with \(1<p<\infty \), illustrating these results with an application, obtaining a generalised compactness by compensation result.

Keywords

Commutator compactness Fourier multiplier H-distribution 

Mathematics Subject Classification

42B15 35B40 28C15 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceUniversity of ZagrebZagrebCroatia
  2. 2.Visage Technologies ABLinköpingSweden
  3. 3.Faculty of MathematicsUniversity of MontenegroPodgoricaMontenegro

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